Question:
The acceleration of a sphere falling through a liquid is \( (30 - 3y) \, \text{cm/s}^2 \) where \( y \) is speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are
The acceleration of a sphere falling through a liquid is \( (30 - 3y) \, \text{cm/s}^2 \) where \( y \) is speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are
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To find the maximum velocity in problems involving acceleration with respect to speed, solve the differential equation for velocity.
Updated On: Jan 12, 2026
- 10 cm/s after 10 second
- 10 cm/s instantly
- 10 cm/s, will never be achieved
- 30 cm/s, after 30 second
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The Correct Option is D
Solution and Explanation
Step 1: Analyze the equation.
The velocity of the sphere can be found by solving the differential equation given by \( a = \frac{dv}{dt} = 30 - 3v \).
Step 2: Conclusion.
Thus, the maximum velocity is 30 cm/s, achieved after 30 seconds.
Final Answer: \[ \boxed{30 \, \text{cm/s, after 30 second}} \]
The velocity of the sphere can be found by solving the differential equation given by \( a = \frac{dv}{dt} = 30 - 3v \).
Step 2: Conclusion.
Thus, the maximum velocity is 30 cm/s, achieved after 30 seconds.
Final Answer: \[ \boxed{30 \, \text{cm/s, after 30 second}} \]
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